Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x-2y &= 2 \\ 3x+4y &= -4\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -3x-4$ Divide both sides by $4$ to isolate $y$ $y = {-\dfrac{3}{4}x - 1}$ Substitute this expression for $y$ in the first equation. $2x-2({-\dfrac{3}{4}x - 1}) = 2$ $2x + \dfrac{3}{2}x + 2 = 2$ Simplify by combining terms, then solve for $x$ $\dfrac{7}{2}x + 2 = 2$ $\dfrac{7}{2}x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $2( 0)-2y = 2$ $-2y = 2$ $-2y = 2$ $y = -1$ The solution is $\enspace x = 0, \enspace y = -1$.